for going that distance that often I honestly would say a 2500 would do you a lot of good, although the Tahoe should do it ok, you will just be much closer to capacity (or slightly over depending on your truck and loaded weight of the unit, and hitch weight)
a camper will have more wind resistance, but I have towed about 8k (03 avalanche on a tandom axle car trailer. est truck at 6k and trailer just shy of 2k ) with my 02 1500 3.73 avalanche about 200 miles, although it did fine, it was more than I would want to do more than a couple times at all. both for ease and durability . it rode/drove fine as it was loaded well and I have an extra cooler, wdh with 1k bars and trailer brakes on both axles.
I later pulled nearly identical load (03 Denali on the same trailer) with my 02 2500 burb ( 8.1, 4.10) and it is a completely different game. chassis, and brakes alone are so much better, then the obvious power with the engine and gear advantage. ( but even with the 6.0 in the wife's denali makes a difference, and gears would just help further. )
that said I don't think I would have any major issues doing it with the Tahoe ( as long as I was not over my legal limits) but it would be at capacity enough to not make a regular trip that enjoyable. enough so that the buddy I got our denali from is why he got it, he had a standard 5.3 Yukon, and got the denali xl for the extra room, more power and better trailer towing for the camper they had. hydraboost definitely helped too.
you say the weight is about 6500, and that is probably dry weight, so loaded will be closer to 7000-7500. plus what every persons and gear you have in the Tahoe. so you will be on the edge of what the truck is rated for.
no matter what you pull it with I would recommend an aftermarket hitch ( the stock ones are known to be weak and kinda suck, have the potential to bend the frame rails when nearing capacity) and be sure everything else is up to ***** and take your time (esp if running a 1500.)
